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ABCD is a parallelogram and ABCE is a cyclic quadrilateral. Find the measure of ∠AEC.

Aakash Shah

In the given figure, ABCD is a parallelogram and ABCE is a cyclic quadrilateral. If ∠ADC=52°, find the measure of ∠AEC.

Parallelogram_ABCD_q_8_b

1 Answer

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Aakash Shah

Given, ABCD is a parallelogram, ABCE is a cyclic quadrilateral and ADC = 52°

To find: The measure of AEC

Here,

(I) ABC = ADC {Being the opposite angles of a parallelogram}

52°

(II) ABC + AEC = 180° {Being opposite angles of a cyclic quardrilateral)

or, 52° + AEC = 180°

or, AEC = 180° - 52°

or, AEC = 128° 

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